Ohm’s Law Survives at the Atomic Scale

Ohm’s Law is extended to the atomic level, and Moore’s Law may get a reprieve

Atomic Bridge: The template for a 1.5-nanometer-wide nanowire was made by pushing atoms around using a scanning tunneling microscope. The resulting nanowire showed that Ohm's Law works even for wires just 4 atoms thick. Click on image to enlarge.

5 January 2012—Moore’s Law, the cornerstone rule of the semiconductor industry, may get a reprieve from its predicted demise, according to a group of scientists in Australia and the United States. Their unexpected findings show that a well-understood law of classical physics—and a pillar of electrical engineering—holds for some objects that are just four atoms wide, a size where quantum effects should rule instead.

Michelle Simmons and her colleagues at the University of New South Wales, in Australia, together with collaborators at the University of Melbourne and Purdue University, in Indiana, have built low-resistance silicon wires that show that Ohm’s Law works at the atomic level. Ohm’s Law, an empirical rule discovered by the German physicist Georg Ohm in 1827, says that the current through a conductor is directly proportional to the potential difference across the conductor. Introducing the concept of resistance, the law is a mainstay of circuit theory and is taught to high school and college students in physics and engineering classes.

In an accompanying commentary in Science, where the research is being reported Friday, Arizona State University’s David Ferry called the finding "surprising." Scientists expected that classical behavior like Ohm’s Law would break down at the atomic level. "The pointlike electron motion of the classical world would be replaced by the spread-out quantum waves. These quantum waves would lead to very different behavior," the IEEE Fellow adds.

Simmons and her collaborators built fine nanowires out of silicon that were just one atom tall, four atoms wide (about 1.5 nanometers), and 106 nm long. They used scanning tunnel microscopy to pattern the wires on a silicon surface and then silicon crystal growth to bury the wires and protect them from surfaces and interfaces that could suck up any free electrons and interfere with Ohm’s Law–like behavior, Simmons says.

Previous experiments had shown that at widths less than 10 nm, the resistivity of silicon nanowires increased exponentially (Ohm’s Law, by contrast, is linear). The researchers were able to get around this exponential increase and follow Ohm’s Law, in effect, by heavily doping the silicon nanowires with phosphorus.

"The phosphorus atoms have one more electron than silicon, and these extra electrons allow the nanowire to conduct," Simmons explains. "Within the wires we place the phosphorous atoms less than 1 nm apart so that the wave functions of the electron overlap to form a metallic-like state, and that gives us this low resistivity."

Electrical engineer John Kymissis of Columbia University was impressed with the experiments. "It avoids all of the interfaces, surface scattering, and grain boundaries" that hampered other approaches, he says. Researchers say that the finding should make it easier for Moore’s Law to maintain its momentum. Today’s high-end chips already must fend off some esoteric quantum effects, and more are expected as engineers continue to shrink IC components. A major challenge to scaling down silicon chips is "the power dissipation from parasitic resistances that cannot be eliminated from current designs and materials," says Dick Slusher, head of the Georgia Tech Quantum Institute. An atomic wire that follows Ohm’s Law could help.

Physicist Steven Simon of Oxford University calls the nanowire "an impressive piece of technology" but says making multiple wires with identical resistivity could get tricky. "Unless one can control exactly where the [phosphorus] impurities are, there may always be outlier samples that don’t conduct at all."

Of course, the experiments by Simmons and colleagues were not done using standard silicon processing techniques, but eventually they might be made to conform to them.

"Fundamentally, we have shown that we can maintain low resistivities in doped silicon wires down to the atomic scale," Simmons says. It may not be ready for production now, but, she says, "who knows 20 years from now?"

About the Author

Saswato R. Das, a New York City–based writer, contributes frequently to IEEE Spectrum. In September 2011 he reported on advances that could bring us closer to practical quantum computing.